Diagnosis of water pipeline systems by frequency domain analysis

Inverse transient analysis is a tool for the diagnosis of water distribution systems based on the comparison of the results of analytical or numerical models with pressure signals acquired during transients. The needed numerical models can be derived in the time domain or in the frequency domain. The time-domain approach is the most followed and leads to the method of characteristics. The traditional models derived in the frequency domain as solutions to the linearized water hammer equations, namely the impulse response and the transfer matrix methods, are efficient in the simulation but are not suited for complex arbitrarily configured networks. An alternative frequency-domain formulation is the network admittance matrix method, where the equations are reorganized into a matrix form using graph-theoretic concepts. In this paper the network admittance matrix method is applied to assess its reliability in the diagnosis of water distribution systems. The unsteady-friction term is introduced in the formulation and a numerical case study is used to detect a pipe replacement in a simple system of metallic pipes. The length, the diameter and the position of the pipe replacement are considered as unknowns and estimated by means of a calibration procedure.